How does the shrimp/algae system illustrate the interaction of photosynthesis and respiration, as well as how a simple ecosystem works

Algae are not really plants, but they do photosynthesis and cellular respiration. Almost all of their cells can do photosynthesis, so they can make a lot of oxygen during the daylight hours.

Explanation:

Plants produce carbon dioxide all the time because of respiration, but during the day (when there is light), they use CO2 for photosynthesis, and fix CO2 into other molecules, giving as end product O2 more than CO2. This is why it is called carbon fixation. On the other hand, when it is dark, plants do not have an energy source for photosynthesis, and so cannot fix CO2 and produce O2. The process is light-independent, and more formally known as the Calvin cycle. During this cycle, 3 carbon dioxide molecules are absorbed to produce the small sugar G3P (glyceraldehyde-3-phosphate) for the plant to use elsewhere. Two G3P molecules are required to make glucose.

As for comparing the amount of carbon dioxide and oxygen between night and day it depends on how you look at the sample region. You can consider anything from the block you live on to the entire Earth. If you only consider your block during the day, large amounts of carbon dioxide are produced from higher activity levels with humans, animals, and driving of vehicles. Additionally at this time, any living plants are producing high amounts of oxygen. At night, plants take in carbon dioxide reducing it's levels; however, humans and animals are still producing it.

When considering these fluctuations between oxygen and carbon dioxide you also have to consider the overall atmosphere composition before you start the "experiment". We start with ~21% Oxygen, and ~0.04% carbon dioxide. Even though there is an increase in carbon dioxide through the daytime on your block, oxygen is much more present at the beginning of the day.

This question really highlights the reason climate change is occurring due to increases in greenhouse gases (carbon dioxide is just one of many). Although plants do a great job of eliminating carbon dioxide, they can't keep up with the additions that we use during the day. If you are interested in looking at the changes in oxygen and carbon dioxide an isolated area, I'll suggest that you look into the Biosphere 2 owned by the University of Arizona. They have completed some really cool research.

Lastly, addressing the idea of taking in oxygen in the morning - since our atmosphere is comprised mostly of nitrogen (~78%) followed by oxygen (~21%) and some other gases (including carbon dioxide), we take in many gases in the morning! If there were no oxygen, then it would be a major health hazard, as we require oxygen to continue life. So overall, even though the concentration of carbon dioxide is increasing, it's levels are many times lower than oxygen.

9.9 years

a = p(1 + rt) . . account balance after time t at rate r starting with principal p

3000 = 2500(1 + 0.0202t) . . filling in the given numbers

1.2 = 1 + 0.0202t . . divide by 2500

0.2 = 0.0202t . . . subtract 1

0.2/0.0202 = t ≈ 9.901

it will take about 9.9 years for the account balance to reach $3000.